Journal of Electrical Engineering & Technology Vol. 5, No. 2, pp. 307~318, 2010 307
Effect of Load Modeling on Low Frequency Current Ripple
in Fuel Cell Generation Systems
Jong-Soo Kim*, Gyu-Yeong Choe*, Hyun-Soo Kang** and Byoung-Kuk Lee†
Abstract – In this work, an accurate analysis of low frequency current ripple in residential fuel cell
power generation systems is performed based on the proposed residential load model and its unique
operation algorithm. Rather than using a constant dc voltage source, a proton exchange membrane fuel
cell (PEMFC) model is implemented in this research so that a system-level analysis considering the
fuel cell stack, power conditioning system (PCS), and the actual load is possible. Using the attained results, a comparative study regarding the discrepancies of low frequency current ripple between a simple resistor load and a realistic residential load is performed. The data indicate that the low frequency
current ripple of the proposed residential load model is increased by more than a factor of two when
compared to the low frequency current ripple of a simple resistor load under identical conditions.
Theoretical analysis, simulation data, and experimental results are provided, along with a model of the
load usage pattern of low frequency current ripples.
Keywords: Low frequency current ripple, Residential load modeling, Rectification load, Power conditioning system, Modeling and simulation
1. Introduction
To reduce global warming and the exhaustion of fossil
fuels, the research and development of new renewable energy sources and related technologies are becoming more
and more relevant. In particular, fuel cell power generation
systems offer a number of advantages, such as high efficiency and regular power generation, when compared to
conventional or other renewable energy sources. Fuel cell
power generation systems are incorporated into numerous
applications, from high-capacity power plants used for grid
connection to low capacity power generators for standalone, transportation, and portable applications. As such,
fuel cell power generation systems must not only meet basic performance levels, but also possess high efficiencies,
high reliability, a long lifetime, and specific safety features
if they are to be implemented in the near future. Although
various factors affect fuel cell systems, the effect of low
frequency current ripple, which is generated from power
conditioning systems (PCSs), has a particular influence on
fuel cell systems [1]-[2].
PCSs are necessary in order to convert the dc power
from a fuel cell into ac power for a commercial frequency
in residential power generation (RPG) systems. Low frequency current ripple components are rectification effects,
which arise from the use of inverter switches, and appear
as a 100 Hz or 120 Hz pulsating current in single-phase
systems. Low frequency current ripples, especially ripple
†
Corresponding Author: School of Information and Communication
Engineering, Sungkyunkwan University, Korea. (bkleeskku@skku.edu)
*
School of Information and Communication Engineering, Sungkyunkwan University, Korea.
** R&D Center, Advanced Drive Technology Co., Ltd., Korea.
(hskang@adtech21.com)
Received: January 13, 2010; Accepted: March 9, 2010
signals of less than 400 Hz, have been the reported cause
of many negative effects, such as: 1) slower cathode surface response, 2) an increase in fuel consumption by more
than 10%, 3) oxygen starvation, 4) a reduction in operating
lifetime, and 5) malfunctions in fuel cell power generation
systems [3], [4]. Accordingly, the limitation standards regarding low frequency current ripple are specified in various technical reports and manufacturers’ manuals. According to the Fuel Cell Handbook (7th Ed., 2004), for 10 kW
systems used for stand-alone fuel cell power generation systems, the 120 Hz ripple component should not exceed 15%
and the 60 Hz ripple component should be limited to 10%
at 10%-100% loads [5]. For example, the Ballard Nexa 1.2
kW PEMFC is set to a 120 Hz current ripple limit of up to
35% of the peak-peak value, or up to 24.7% of the root
mean square (rms) value [6]. The 120 Hz ripple, which
arises under stand-alone loads in single-phase systems, is
strictly regulated. In a three-phase system, the lowest current ripple appears as 360 Hz and the ripple size is much
smaller than that found in a single-phase system due to the
phase overlap. Residential loads are primarily rectification
loads applied to a single-phase source and can be considered as the worst condition from a low frequency ripple
point of view. Therefore, consideration of a single-phase
RPG system, which is mainly a rectification load, is essential.
To improve the performance of a fuel cell stack, research
in the power electronics field has been carried out in an
attempt to reduce low frequency current ripple. To reduce
the ripple, a design methodology was proposed in [7] so as
to select the required capacity of a passive energy storage
component, such as a capacitor. In addition, an advanced
active control technique was proposed in [7] to incorporate
a current control loop in a dc-dc converter. In particular, an
active control technique presented the possibility for reduc-
308
Effect of Load Modeling on Low Frequency Current Ripple in Fuel Cell Generation Systems
ing ripple currents by employing a control strategy instead
of additional hardware components. An impedance model
of the fuel cell stack was also proposed in order to evaluate
the effects of current ripple [8]. On the other hand, a technique was proposed to minimize input ripple current in a
three-phase pwm inverter when unbalanced/nonlinear loads
are supplied [9]. The proposed technique has the advantage
of reducing ripple currents in unbalanced load conditions.
However, such a technique is not applicable to single-phase
systems, such as those found in residential applications.
One drawback of previous research on ripple current was
that the studies were carried out under simple load conditions using only a resistor. Such experiments do not represent actual residential load conditions. In RPG systems, the
fuel cell system powers several home appliance loads such
as an air-conditioner, a refrigerator, a TV, a computer, and
so on. These are mostly rectification loads, not resistor
loads, which mean that an analysis of the generation pattern of low frequency current ripples must be carried out
for practical residential load models.
In order to analyze the generation pattern of low frequency current ripple, the authors propose a new residential load model in this work. To develop the proposed residential load model, representative home appliances are
selected and their electrical characteristics are modeled by
a combination of R-L-C components. Furthermore, the
daily load usage pattern is then realized using a specific
switching algorithm so that the generation pattern of the
low frequency current ripples, according to a 24-hour operation pattern, can be analyzed. For an accurate analysis, a
PEMFC model is implemented instead of using a constant
dc voltage source, so that a system-level analysis considering the fuel cell stack, power conditioning system, and actual load is possible. In Section VI, the influence of load
conditions and the effect of PCS topological structures and
their constituent power electronics devices are analyzed. A
detailed theoretical explanation of the proposed model and
algorithm is also presented, along with the results of simulation and experiments.
shown in Fig. 2(c). The filtered output voltage and current
of the inverter are expressed in (1) and (2).
vo (t ) = Vm cos(ωt + θ )
io (t ) = I m cos(ωt + φ )
(1)
(2)
where, θ and φ represent phase angles.
The generation and propagation mechanism of low frequency current ripple can be explained using the energy
conservation law. The angular frequencies of the output
voltage and current are both ωt, and the output power is
calculated by multiplying (1) and (2). The frequency of the
output power of a single-phase inverter has twice the angular frequency of 2ωt, and can be derived as shown in (3).
Pout (t ) = (Vm I m / 2 ) {cos ( 2ωt + θ + φ ) + cos (θ − φ )}
(3)
Based on the energy conservation law described in (4)
and neglecting inverter power dissipation, the powers at the
dc link and the ac output should be identical.
Vd I d* (t ) = vo (t )io (t )
(4)
where, I*d is the filtered dc link current, which consists of a
pure dc component and a sinusoidal component at twice
the fundamental frequency. The Id term is the inverter input
current, which consists of I*d and the high frequency components due to inverter switchings.
Fig. 1. Block diagram of power conditioning system for
fuel cell.
2. Analysis of Low Frequency Current Ripples
To examine the generation and propagation of low frequency current ripple according to the load conditions, a
single-phase RPG system was considered. As shown in Fig.
1, the system consists of a step-up full bridge dc-dc converter and a single-phase inverter.
2.1 Generation and Propagation Mechanism of Low
Frequency Current Ripple
Unipolar sinusoidal pwm (spwm), as shown in Fig. 2(a),
is commonly used for single-phase inverters. The output
voltage appears as a pulsating waveform, as shown in Fig.
2(b). For connection at the grid, a low pass LC filter is
used to eliminate high frequency components. The final
output voltage becomes a 60 Hz sinusoidal waveform, as
Fig. 2. Operation principle of unipolar sinusoidal pulse
width modulation: (a) Reference and carrier waveforms, (b) pwm output voltage before filtering, and
(c) Sinusoidal output voltage with LC filter.
Jong-Soo Kim, Gyu-Yeong Choe, Hyun-Soo Kang and Byoung-Kuk Lee
I d*
= (Vm I m / 2Vd ) {cos ( 2ωt + θ + φ ) + cos (θ − φ )}
H+
H+
H+
H+
H+
H+
(5)
Electrolyte
When (3) and (4) are properly rearranged, the frequency
and shape of the dc link current (I*d) is the same as the
counterparts of the output power. The dc link current can
then be expressed as (5) because the dc link voltage is generally regulated by the voltage controller of the dc-dc converter.
H+
309
eeeeeee-
(a)
When the converter loss is neglected, the fuel cell current
(IFC) shows a 120 Hz ripple component on top of the pulsating dc current. This is due to the switching behavior of
the full bridge dc-dc converter, as described by (6).
I FC = Vd I d* / Vstack
⎛
⎛ i + in ⎞ RT ⎛ i + in
RT
Vstack _ static = N ⎜ E − ( i + in ) r −
ln ⎜
ln ⎜
⎟+
⎜
F
2
α
⎝ iec ⎠ 2 F ⎝ iL
⎝
Fig. 3. Charge double layer of a fuel cell: (a) Equivalent
model at the surface of a fuel cell cathode, and (b)
Electrical equivalent circuit of a unit cell.
Vstack = E − Vohmic − vc
(6)
where, Vstack is the output voltage of the fuel cell stack.
The output voltage of the fuel cell stack has both static
and dynamic characteristics. For the static characteristics,
the operating voltage of the fuel cell stack, as described by
(7), is the Nernst voltage minus the activation, ohmic, and
concentration polarizations.
⎞⎞
⎟ ⎟⎟
⎠⎠
(7)
where, N is the number of cells, E is the Nernst voltage, i is
the current density, in denotes the internal current density, r
is the sum of the ionic, electronic, and contact resistance, R
represents the gas constant, T is the temperature in K, α is
the transfer coefficient, F is Faraday’s constant, iec denotes
the exchange current density, and iL is the limit current density.
A practical fuel cell stack has dynamic characteristics.
An equivalent electrical model indicating the dynamic characteristics of a unit cell can be presented as an RC firstorder time delay circuit, as shown in Fig. 3. This characteristic is called the “charge double layer” phenomenon. In
this phenomenon, potential differences, caused by the accumulation of hydrogen ions and electrons on both sides of
an electrolyte, arise while gathering the responsive minimum gas density [10]. The voltage loss (vc) and time constant (τ) due to the charge double layer can be derived as
shown in (8) and (9), respectively.
dvc / dt = (i / Ccdy ) − (vc / τ )
(8)
τ = Ccdy Ra = ⎡⎣Ccdy (Vact + Vcon ) ⎤⎦ / i
(9)
where, vc is the voltage loss due to the charge double layer,
Ccdy is an equivalent capacitance, τ is the time constant, Ra
denotes the sum of the activation polarization resistance
and the concentration polarization resistance, Vact is the
activation polarization, and Vcon is the concentration polarization.
Consequently, the fuel cell stack voltage (Vstack) can be
expressed as shown in (10) [10]-[12].
(b)
(10)
where, Vohmic is ohmic polarization.
2.2 Analysis of Low Frequency Current Ripples
According to the Load Conditions
When a pure resistor load is connected to a single-phase
PCS system, the inverter output current (io) becomes a sinusoidal waveform that is in-phase with the output voltage
(vo) and has the same frequency as ωt. Therefore, the phase
angles of θ and φ become zero in (1)-(3). The output power
is always a positive value; it has a dc value, twice the output current frequency, and a small high frequency component. Figs. 4(a) and (b) depict the equivalent circuit, voltage, and current waveforms when a pure resistor load is
connected to the inverter.
The rectification load is a load which includes a rectifier.
The rectifier needs to convert ac into dc in order to supply
Ls
Rs
vo
io
vo
RL
(a)
(b)
Fig. 4. (a) Equivalent circuit under simple resistor load
condition, and (b) Voltage and current waveforms
under simple resistor load condition.
Effect of Load Modeling on Low Frequency Current Ripple in Fuel Cell Generation Systems
power, of variable voltage and/or frequency, from a source
of constant voltage and frequency. Most home appliances
have this kind of rectification load. The load consists of a
power conversion system that includes a diode rectifier,
filter capacitor, dc-dc converter, and an inverter at the load
side which can be represented as a resistive, inductive, or
capacitive load. The inverter current of the PCS is chosen
to be in compliance with the electrical potential difference
of the input voltage and the output voltage of the rectification load. This means that the inverter output waveforms of
the fuel cell PCS are very complicated when compared to a
simple resistor load condition.
Figs. 5(a) and (b) depict the practical circuit and an
equivalent circuit of the rectification load, respectively. A
line inductance (Ls) and resistance (Rs) are included in the
circuit because a long cable is generally required to connect the PCS output terminal to the load. The final load
(Rload) behind a dc link capacitor (Cd) can be modeled using
a pure resistor. Shown in Fig. 6 are the voltage and current
waveforms at the rectification load.
In Mode 1 (t0<t<t1) and Mode 4 (t3<t<t4), the dc link
voltage and current are given by (11) and (12), respectively.
dvload / dt = −(vload / Cload Rload )
(14)
The complete voltage and current equations of the dc
link can be expressed by (15) and (16), respectively [13].
id
+
Rs
Rload
ㅡ
(a)
Ls
id
Rs
vload
|vo|
RL
(b)
Fig. 5. (a) Practical circuit under rectification load condition, and (b) Equivalent circuit under rectification
load condition.
Inverter
id = Cload ( dvload / dt ) + (vload / Rload )
DC Link
(13)
io
(
Fig. 6. Voltage and current waveforms under rectification
load condition.
Fuel Cell
vo = Rs id + Ls ( did / dt ) + vload
vo
)
A large nonlinear current is generated when the rectification loads are connected to the PCS. As such, the peak current becomes much greater than that found in the simple
resistor load condition, even if the average current is identical. For this reason, a much larger low frequency current
ripple affects the fuel cell stack, as analyzed in Section 2.1.
Figs. 7(a) and (b) show aspects of the generation and propagation of low frequency current ripples for simple resistor
load and rectification load conditions, respectively.
Inverter
In Mode 2 (t1<t<t2) and Mode 3 (t2<t<t3), the dc link
voltage and current equations are given by (13) and (14),
respectively.
vload
(
(16)
DC Link
(12)
Cload
id = Cload
(15)
d
1
vd (t3 / ω )e − ( t − t3 / ω ) /(Cload Rload ) +
vload (t3 / ω )e − (t − t3 / ω ) /( Cload Rload )
dt
Rload
(11)
id = 0
Ls
vload (t ) = vload (t3 / ω )e − (t −t3 / ω ) /(Cload Rload )
Fuel Cell
310
Po
Pdc
PFC
vo io
Vd id
VFCIFC
Time[ms]
(a)
Po
Pdc
PFC
vo io
Vd id
IFC VFC
Time[ms]
(b)
Fig. 7. Aspect of generation and propagation of low frequency current ripples: (a) Under simple resistor
load condition, and (b) Under rectification load
condition.
)
Jong-Soo Kim, Gyu-Yeong Choe, Hyun-Soo Kang and Byoung-Kuk Lee
3. Modeling of a Residential Load and
a 24-hour Operation Pattern
3.2 Modeling of a Daily Residential Load Profile
3.1 Electrical Modeling of a Practical Residential
Load
Most loads used in an ordinary household are rectification loads. According to a recent project in Korea, six representative home appliances such as refrigerators, TVs,
electric rice cookers, computers, washing machines, and
air-conditioners are selected as the load for this study [14].
Table 1 shows the detailed power consumption, watthours, daily usage times, and electrical models of specific
home appliances. One such appliance, a 680 liter class refrigerator (SRT686UTCE: Samsung Electronics Company)
uses around 60 kW of power per month in common usage.
Since the refrigerator is operating all day, it has an average
daily power consumption of 1.992 kW. Assuming 83 W of
power is consumed per hour, the load impedance can be
calculated as 1,157 ohms. The refrigerator can be modeled as
a rectifier, dc link capacitors, and a load, which is the motor’s impedance for the compressor (which can be modeled by
a pure resistor). A Samsung Electronics plasma display
panel (PDP), the SPD-42Q92HD, was also analyzed and its
rated power consumption is about 410 Wh. The PDP also
includes a rectifier in order to convert power from ac to dc
because a high voltage is required to generate the plasma.
The electric rice cooker, computer, washing machine, and
air-conditioner are modeled on the same principle, reflecting
their practical characteristics.
Table 1. Electrical characteristics and modeling of residential loads
Refrigerator
TV
Rice cooker
(warming /
cooking)
PC
+Monitor
Washing
machine
Airconditioner
Lighting
Watt-hour
(Wh)
83
410
Daily
usage(h)
24
6
Electrical
model
C+RL
C+R
135 /
1,100
15 / 0.5
240 + 38
R (Ω)
C (uF)
1,157
234
680
680
R
711 /
87
-
5
C+R
345
680
150
1
C+RL
640
680
2,600
1
C+RL
36
680
150
8
R
640
-
Fig. 8 shows a weekday demand load curve for an ordinary household for each of the four seasons. These data
were provided by the Korea Energy Management Corporation (KEMCO) for each of the four seasons [15].
The general pattern of home appliance power consumption is that more power is used in the morning and after
sunset. Power consumption during different seasons seems
to indicate an increase during the summer, with increased
lighting loads during the autumn months. The load pattern
during spring can be considered to be the load between the
summer and the autumn seasons. Therefore, the peak power consumption appears in the summer season after sunset.
In this research, home appliance consumption patterns during the summer were selected for analysis.
Demand Load Usage Pattern
1600
[Confrontation Coefficient]
As previously mentioned, low frequency ripples vary by
the load conditions, even if the system specifications and
operating conditions are identical. Therefore, modeling of
practical loads is strongly required so as to properly design
and examine the performance of the PCS for the RPG system. In this section, the electrical modeling of a practical
residential load is implemented. Low frequency ripple,
according to the time utilization of residential loads during
the day, are analyzed by considering models of the load
usage pattern of an ordinary household [1].
Item
311
1400
1200
1000
800
Spring
Summer
600
Autumn
Winter
400
2
4
6
8
10
12
[Time]
14
16
18
20
22
24
Fig. 8. Daily demand load usage pattern of ordinary household in Korea according to seasons.
3.3 Implementation of a Residential Load Bank
By combining the electrical modeling of residential
loads with the daily residential load pattern in Sections 3.1
and 3.2, a residential load bank was implemented using a
PSIM 6.0 simulation program. The daily residential load
pattern, shown in Fig. 9, was realized using Gating Block
for Switch, a function of PSIM [16]. It is usually necessary
to include at least three or four cycles of a periodic wave in
order to analyze its harmonics [17]. Therefore, to analyze
the 120 Hz ripple, the minimum sampling period must be:
TSP ≥ 3 / f S ,120 Hz
(17)
where, TSP is minimum sampling period.
Among the loads, the shortest operation time was set to
30 min for the cooking mode of the electric rice-cookers.
The minimum required simulation time to analyze at least
three cycles of the 120 Hz ripple can be expressed as:
TSim ≥ ( 3 / f S ,120 Hz ) ⋅ ( 24 / tload ,min )
(18)
where, TSim is the entire simulation time, and is the minimum operation time of the loads.
Effect of Load Modeling on Low Frequency Current Ripple in Fuel Cell Generation Systems
312
To acquire reliable harmonics data, the 24-hour period
must be scaled down into slightly more than 1.2 s. Consequently, the simulation time was set at 2 s, and the gating
time was converted from 1 hour into 15 degrees by using
the Gating Block for the Switch. To provide reasonable
results for the simulation conditions, ripple variation due to
a load change was examined in the six modes. This means
that one mode represented 4 hours.
Refrigerator
TV
Rice cooker
PC
Washing
Table 2. PCS simulation parameters
Parameters
Maximum power
Fuel cell voltage
DC Link voltage
Output voltage
Converter switching frequency
Inverter switching frequency
DC link capacitor
Output filter capacitor
Load capacitor
DC link inductor
Output filter inductor
Symbols
P
Vfc
Vdclink
Vout
fswc
fswi
Cd
Co
Cload
L
Lo
Value [unit]
3.844 [kW]
26-45 [Vdc]
380 [Vdc]
220 [Vac]
60 [kHz]
10 [kHz]
3,360 [uF]
5 [uF]
3,400 [uF]
1 [mH]
3 [mH]
Air-Cond.
Lighting
0
A day
Simulation time 0
Gating degree 0
Mode
Time
2
4
6
8
10
30
60
90
120
150
MODE I
0-4
MODE II
4-8
MODE III
8 - 12
12
1
180
14
16
18
20
210
240
270
300
MODE IV
12 -16
MODE V
16 - 20
22
330
24 Hour
2
Sec
360 Degree
MODE VI
20 - 24
Fig. 9. Load profile of 6-home appliances scaled down 24
hours to 2 sec and 360degrees.
4. Simulation Results
The validity of the theoretical analysis of low frequency
current ripple under the proposed residential load condition
was verified by both computer simulation and experiments.
Details of the simulation circuit and parameters are
shown in Fig. 10 and Table 2, respectively. As previously
mentioned, the generation of low frequency current ripple
is independent of the characteristics of the fuel cell stack;
such characteristics include the flow-field pattern, gas-flow
between cells, gas channel geometry sizes, and so on.
However, for an accurate analysis of an entire fuel cell
generation system, the Ballard Nexa 1.2 kW PEMFC stack
was used because it is a well-known and highly reliable
fuel cell stack [6]. The nonlinear V-I characteristics and
dynamic characteristics due to the charge double layer effect of the PEMFC stack were modeled in Matlab/Simulink.
The power conversion circuit and the proposed residential
load model were implemented using a PSIM simulation
tool. Therefore, in this work, Matlab/Simulink and PSIM
Out1
p_h2
Out2
p_o2
Out3
p_h2o
Out4
p
were used interchangeably so as to analyze the exact ripple
current phenomena.
The characteristics of the fuel cell stack voltage exhibit
exponential behavior due to a double-layer effect at the
load step changes. These characteristics are detailed by the
electro-chemical equations described in (7)-(10). Fig. 11
shows the static and dynamic characteristics, at the load
step changes. Detailed simulation parameters of fuel cell
stack are described in Table 3.
Fig. 12(a) shows the fuel cell, dc link and inverter current for a constant pure resistor load at 1 kW. Fig. 12(b)
depicts the harmonics spectrum of the fuel cell current,
specifically at the 120 Hz ripple. The fundamental and 120
Hz components of the fuel cell current are 26.12 A and
5.48 A, respectively. Therefore, approximately 20% of the
120 Hz ripple was generated.
The fuel cell current and other waveforms for a rectification load instead of the simple resistor load are shown in
Fig. 13(a) and the harmonics spectrum is shown in Fig.
13(b). The fundamental and 120 Hz components of the fuel
cell current are 22.44 A and 8.52 A, respectively. Therefore,
about 38% of the 120Hz ripple was generated. Although
the system power under each load condition was identical,
the peak current was considerably increased by more than
150% with approximately 50 A, even when the average
current of the fuel cell was the same. This increase was due
to large nonlinear current.
Power Conditioning System
In4
Mass
Flow
Controller
stack_v ol
i
Scope
PEMFC
-KCurrent Scale
Fig. 10. Simulation circuit to analyze low frequency current ripples.
Jong-Soo Kim, Gyu-Yeong Choe, Hyun-Soo Kang and Byoung-Kuk Lee
45
Fuel Cell Voltage
35
25
20
Fuel Cell Current
10
0
0
0.25
0.5
0.75
Time[s]
1
Fig. 11. Dynamic characteristics of fuel cell stack due to
charge double layer.
60
Fuel Cell Current
30
0
40
DC Link Current
15
-10
400
Inverter Output Voltage
Inverter Output Current
0
-400
0
20
40
Time[ms]
60
80
100
(a)
30
Fundamental component
120Hz ripple component
15
0
0
100
200
Frequency [Hz]
300
Table 3. Fuel Cell Modeling Simulation parameters [10]
Parameters
Nernst voltage
Internal current density
Resistance
Gas constant
Temperature
Faraday’s constant
Exchange current density
Number of cells
Resistance of charge double layer
Capacitance of charge double layer
Symbols
E
in
r
R
T
F
iec
N
Ra
Ccdy
Value [unit]
1.229 [V]
2 [mA.cm-2]
0.1 [ohm.cm-2]
8.3144 [J.mol K-1]
343.15 [K]
96,485 [C.mol-1]
0.0017 [mA.cm-2]
48
0.1 [ohm.cm-2]
0.6 [F]
Using the developed simulation model of the fuel cell
stack, current trajectories of the fuel cell stack according to
the load conditions are shown in Fig. 14. For a simple resistor load, the range of current fluctuation was from approximately 22 A to 32 A.
For the rectification load, the current fluctuation was
even larger and ranged from about 12 A to 46 A. Such high
current directly harms the fuel cell stack in that it creates
oxygen starvation and causes an increase in fuel consumption. This is because the fuel cell operates in the mass
transportation region. Because the maximum permissible
stack current is 46 A, nuisance tripping, such as in an overload situation, can also occur due to a sudden voltage drop.
The generation ratio of the low frequency current ripple
is changed by the capacitance of the rectification load.
However, because voltage ripple due to capacitance is reduced exponentially, a variation in the ratio is not significant when the capacitance is above a certain value. Fig. 15
400
(b)
F uel C ell C u rren t T rajectory accord ing to L oad C on ditio ns (120Hz cu rren t rip ple)
50
Fuel Cell Current
30
un der simple resisto r load
un der prop osed realistic lo ad mod el
Fuel Cell Voltage [V]
Fig. 12. (a) Fuel cell current, dc link current, inverter voltage
and current under simple resistor load condition,
and (b) Harmonic spectrum of the fuel cell current.
60
313
40
30
20
10
0
0
10
40
15
-10
400
Inverter Output Voltage
Inverter Output Current
25
30
35
Fuel Cell Current [A]
40
45
50
30
40
Time[ms]
60
80
100
Fundamental component
120Hz ripple component
15
0
Frequency [Hz]
(b)
Fig. 13. (a) Fuel cell current, dc link current, inverter voltage
and current under rectification load condition, and
(b) Harmonic spectrum of the fuel cell current.
120Hz harm onics [% ]
20
(a)
30
20
Fig. 14. Fuel cell current trajectories according to load conditions.
0
-400
0
15
DC Link Current
25
h120Hz / fundamental
20
15
10
5
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
Load capacitance [uF]
Fig. 15. 120Hz ripple components according to load capacitances.
Effect of Load Modeling on Low Frequency Current Ripple in Fuel Cell Generation Systems
314
150
MODE I
Fuel Cell Current
MODE III
MODE II
-10
Inverter Output Voltage
400
Inverter Output Current
0
-400
0
0.33 0.33
Time[s]
0.66 0.66
Time[s]
MODE IV
1
1.33 1.33
Time[s]
1
Time[s]
MODE V
MODE VI
1.66 1.66
Time[s]
2
Time[s]
Fig. 16. Fuel cell current and distribution of low frequency current ripples according to daily load variation.
40
shows the ratio of 120 Hz ripple components according to
load capacitance. There was no real influence on the ripple
when the capacitance was greater than 3,200 uF.
Fig. 16 shows the simulation results of a downscaled
daily load variation for the ordinary household modeled in
Figs. 8 and 9. From these data, the authors determined the
aspect and distribution of the generation of daily low frequency current ripple in an ordinary household.
Fig. 17 shows the results of the analysis of a 120 Hz
harmonic at a simple resistor load with the proposed practical residential load model under the same operation conditions. The 120 Hz ripple component with the proposed
rectification loads is lowest, at 27.5%, during the period
from 12:00-4:00 p.m., which are the least busy hours
(Mode IV). The 120 Hz ripple component is highest, at
41.8%, after 8:00 p.m., which are the busiest hours (Mode
V). In particular, between 8:00 p.m. and 10:00 p.m. (the
timeframe of the busiest hours (MODE VI)), 45% of the
120 Hz ripple, which is equivalent to 31.04 A, was generated while the fundamental component was 68.49 A. In
conclusion, the pattern and amount of the 120 Hz ripple
current showed totally different behavior when the simple
resistor load was replaced by a realistic rectification load
under the same conditions.
Fig. 18 shows the dc link capacitance required to reduce
the 120 Hz current ripple at the rectification load by as
120Hz harmonics [%]
Fig. 17. Daily distribution of 120Hz harmonic component
under simple resistor load and under proposed
practical residential loads model.
4000
5000
6000
7000
8000
9000
120Hz harmonics [%]
5. Experimental Verification and Discussion
10
V
10
much as the current ripple at the simple resistor load. A 120
Hz ripple component was measured to be 21% under a
simple resistor load when a 3,360 uF dc link capacitor was
used. In the case of the rectification load, in order to keep
the 120 Hz ripple at the same magnitude as in the simple
resistor load condition, a 6,000 uF dc link capacitor was
required. This value is approximately 1.8 times higher than
that used for the resistor load condition. Since 45% of the
120 Hz ripple was generated under the maximum load
condition, a dc link capacitor which is three times larger is
required to reduce the 120 Hz ripple to a level under the
simple resistor load.
20
IV
15
Fig. 18. Required dc link capacitance to reduce.
30
III
20
DC Link Capacitance [uF]
40
II
25
0
under Simple resistor load
under Proposed rectification load bank
I
30
5
50
0
Resistor load (@3360uF of dc link capacitor)
Rectification load according to capacitance
35
VI
The validity of the theoretical analysis and the simulation results of the low frequency current ripple under the
proposed residential load condition has been verified by
experiment. A laboratory prototype of a 1 kW FC-PCS,
which consists of a voltage-fed full-bridge dc-dc converter
and a single phase full-bridge inverter (as shown in Fig.
19(a)) is implemented. The main controller is a MCP56F803
16-bit fixed point processor by Freescale and the analog
pwm controller, adopted for dc-dc converter control, is a
TL494 by Texas Instruments. The experimental setup
shown in Fig. 19(b) is then built up by the 1.2 kW Ballard
Nexa PEMFC with an input power source and load banks.
The load banks are implemented by pure resistors for the
simple resistive load condition and an ac-dc diode rectifier
Jong-Soo Kim, Gyu-Yeong Choe, Hyun-Soo Kang and Byoung-Kuk Lee
315
1kW Fuel Cell Stack
1k W FC- PCS
Host PC &
Power Analyzer
Ch1 : Fuel Cell Current (IFC)
1kW FC-PCS
Load bank
(a)
(b)
Ch2 : Inverter Current (io)
Ch3 : Inverter Voltage (vo)
Fig. 19. Experimental setup.
module with load capacitors for the rectification load condition. The load capacity is determined as 1 kW of the
maximum power and is divided by six modes, as simulation result in Fig. 16, in order to simulate realistic residential loads and load usage patterns. Details of the parameters
of the system and the load bank are listed in Tables 4 and 5,
respectively. A WT3000 power analyzer by YOKOGAWA
is used to analyze the harmonic components of the fuel cell
current.
Fig. 20(a) shows the fuel cell current, including the low
frequency ripple components in the simple resistor load, at 1 kW.
The fuel cell current has approximately 24.1% of the 120 Hz.
Fig. 20(b) displays the fuel cell current in the rectification load (instead of the simple resistor load) even if other
conditions are identical. Due to the load capacitors of the
ac-dc diode rectifier, the inverter current has a snappy, nonlinear shape. The 120 Hz ripple component appears larger
than the simple resistor load condition. It is generated approximately 37.6% of the resistor load condition. The 120
Hz ripple component is considerably increased by more
than 156% because of the huge nonlinear current.
Table 4. PCS Hardware parameters
Parameters
Rated power
Fuel cell voltage variation
Rated DC Link voltage
Rated Output voltage
Converter switching frequency
Inverter switching frequency
DC link capacitor
Output filter capacitor
Load capacitor
DC link inductor
Output filter inductor
Symbols
P
Vfc
Vdclink
Vout
fswc
fswi
Cd
Co
Cload
L
Lo
Value [unit]
1.2 [kW]
26-45 [Vdc]
380 [Vdc]
220 [Vac]
60 [kHz]
10 [kHz]
3,400 -6,800[uF]
5 [uF]
3,400 [uF]
1 [mH]
3 [mH]
Table 5. Load bank parameters
Modes [Capacity]
Mode I
Mode II
Mode III
Mode IV
Mode V
Mode VI
[500W]
[100W]
[250W]
[100W]
[1,000W]
[500W]
Simple
R-Load [Ω]
100
480
200
480
50
100
Realistic Rectification Load
Cload [uF]
Value [Ω]
200
800
400
3,400
800
100
200
(a)
Ch1 : Fuel Cell Current (IFC)
Ch3 : Inverter Voltage (vo)
Ch2 : Inverter Current (io)
(b)
Fig. 20. Fuel cell current, inverter output current and voltage waveforms at 1kW load condition: (a) Under
simple resistor load, and (b) Under rectification
load. (ch1: 20[A/div]; ch2: 10[A/div]; ch3: 350
[V/div]; 20[ms/div]).
Figs. 21(a)-(f) show the generation aspects of low frequency current ripples when a simplified daily load pattern
is applied using a rectification load. The 120 Hz ripple
component is obviously generated more than 20% in entire
operation modes.
Figs. 22(a)-(d) show the reduction aspects of low frequency current ripples according to the dc link capacitances at a 500 W test condition. The dc link capacitors are
680 uF/400 WV electrolyte capacitors composed with 5 to
10 in parallels. This enables the use of 3,400 uF to 6,800
uF dc link capacitances. The results indicate that more than
5,440 uF of dc link capacitance is required to reduce the
120 Hz ripple to a level that is as low as the ripple under
the simple resistor load at 500 W.
The minor disparities between the results of the simulation and the experiment appear to arise mainly from the
lower crest factor, which is in turn due to the huge nonlinear inverter current. In addition, the distribution of the resistor values is limited because physical metal-clad resistors were used. As a result, mismatch among resistor values
between the simulation model and the experiments exists.
Line (or stray) inductance and parasitic capacitances are
also present in the experimental setup. Nevertheless, the
experimental results indicate almost the same aspect of low
frequency current ripples as that found through analysis
and simulation, especially for the 120 Hz component.
Therefore, a fuel cell system, which is used in an RPG application with a stand-alone type, should be considered to
have relatively high current ripples, as observed in the re-
Effect of Load Modeling on Low Frequency Current Ripple in Fuel Cell Generation Systems
316
Ch1 : Fuel Cell Current (IFC)
Ch2 : Inverter Current (io)
Ch3 : Inverter Voltage (vo)
(a)
(b)
(d)
(c)
(e)
(f)
Fig. 21. Fuel cell current, inverter output current and voltage waveforms according to daily load variation under rectification
load: (a) Mode I with 500W, (b) Mode I and II with 100W, (c) Mode II with 250W, (d) Mode III-V with 100W, (e)
Mode VI with 1kW, and (f) Mode VI with 500W. (ch1: 20[A/div]; ch2: 10[A/div]; ch3: 350[V/div]; 20[ms/div]).
Ch1 : Fu el Cell Current (I FC)
Ch2 : Inverter Current (io )
Ch3 : Inverter Voltage (v o )
(a)
(b)
(c)
(d)
Fig. 22. Decreasing of low frequency current ripple according dc link capacitances at 500W condition: (a) At 3,400uF, (b)
At 5,440uF, (c) At 6,120uF, and (d) At 6,800uF. (ch1: 20[A/div]; ch2: 10[A/div]; ch3: 350[V/div]; 20[ms/div]).
sults of this study. It should also be considered during research on ripple reduction.
6. Discussion of Other Factors: Power Electronic
Topologies and Devices
Although the topological structures and power electronics devices of the PCS are generally determined according
to the capacity of an RPG system, the effects of PCS topologies and related power electronics devices should be
considered. In this section, assuming the same residential
load, the effects of other factors, such as PCS topological
structures and energy storage devices (such as capacitors
and inductors), are examined.
While the topology of a single-phase inverter is mostly a
full-bridge type with 4-switches, pwm switching strategies
have different options, such as bipolar and unipolar spwm.
The pwm strategies affect high frequency ripple components rather than low frequency current ripples. Thus, the
effect of topological structures and the pwm switching
strategies of the inverter can be ignored.
The dc-dc converters have numerous topological structures. Among these, a step-up full-bridge converter, a boost
converter, and a push-pull converter are suitable for RPG
applications when considering the low voltage characteristic of the fuel cell stacks and a system capacity of around 1
Jong-Soo Kim, Gyu-Yeong Choe, Hyun-Soo Kang and Byoung-Kuk Lee
kW to 5 kW [4]. These converters can be classified into
two groups: isolation types and energy storage devices. In
this study, a boost converter, which represents a nonisolated and current-fed type dc-dc converter, and a voltage-fed full-bridge converter, which represents an isolated
and voltage-fed converter, were adopted. The input current
of the boost and full-bridge converters were determined by
the duty ratio, output current, and turns ratio of a transformer (for the full-bridge converter only). Therefore, the
topological structures of the dc-dc converters also do not
affect low frequency current ripples.
To analyze the effect of energy storage capacitors, the
fuel cell current can be derived as function of dc link capacitance (Cd) by rearranging (4)-(6) as follows:
iFC ( t ) =
1
⎡Vo,rms I o,rms cos (θ − φ ) + Vo, rms I o , rms cos ( 2ω t + θ + φ )
VFC ⎣
−
−
Vo, rms I o, rms cos ( 2ω t + θ + φ ) cos (θ − φ )
2ω Cd Vd2
(Vo,rms Io,rms )
sin ( 4ω t + 2 (θ + φ ) ) ⎤
⎥
⎥
4ω Cd Vd2
⎦
2
(19)
This result indicates that low frequency current ripples
are significantly affected by the energy storage capacitors
in an inversely proportional manner. Fig. 23(a) shows the
correlation between the magnitude of a 120 Hz ripple and
the capacitance when compared to mathematical analysis
and simulation results.
M agnitude of 120H z Current Ripple [PU]
1.0
Fig. 24 shows the fuel cell current of the boost converter,
including the switching and low frequency ripples. In order
to analyze the effect of energy storage inductors, the fuel
cell current can be derived as a function of the inductance
(L) as follows:
I max.a + I min.a +1 I max.a + I min.a
−
=
2
2
− Vo, rms I o ,rms
(
)
(
cos 2ωT * ( a + 1) + θ + φ − cos 2ωT * ( a + D ) + θ + φ
)
8ω LCd Vd
(20)
As in the case of the capacitance, low frequency current
ripples are affected by the energy storage inductors in an
inversely proportional manner. Fig. 23(b) shows the correlation between the magnitude of a 120 Hz ripple and the
inductance when compared to mathematical analysis and
simulation results. The results of the mathematical analysis
are in good agreement with the simulation results.
The analysis results indicate that the topological structures of the PCS do not influence low frequency current
ripples. However, the energy storage devices in the PCS,
such as the capacitors and inductors, can have a significant
influence on low frequency current ripples.
i (t )
FC
imax.a +1
⋅⋅⋅⋅⋅⋅⋅⋅⋅
based on mathmatical analysis
based on Psim Simulation Results
0.9
317
imax.a
imin.a + 2
0.8
⋅⋅⋅⋅⋅⋅⋅⋅⋅
imin.a +1
0.7
0.6
imin.a
0.5
0.4
SWoff SWoff
SWon SWon
0.3
0.2
0.1
aT *
0
0.1
0.2
0.3
0.4
0.5
0.6
Energy Storage Capacitance [mF]
0.7
0.8
0.9
1
(a)
M agnitude of 120Hz Current Ripple [PU]
1.0
(a + 1)T * (a + 2)T *
t
Fig. 24. Fuel cell current including low frequency and
switching ripples.
based on methmatical analysis
based on Psim Simulation Results
0.9
0.8
7. Conclusion
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0
0.1
0.2
0.3
0.4
0.5
0.6
Energy Storage Inductance [mH]
0.7
0.8
0.9
1
(b)
Fig. 23. Comparison results between derived equations and
PSIM simulation results: (a) In case of capacitors,
and (b) In case of inductors.
In this work, the generation and propagation of low frequency current ripples generated by a PCS for fuel cells
were analyzed. The generation aspects of ripple current
under simple resistor and rectification loads were also studied. A residential load model was developed, along with a
daily demand load pattern. It was proposed that a realistic
load model should be considered for the reduction and/or
elimination of low frequency current ripple. It is expected
that the analysis and the proposed model will be useful in
the optimal design of a PCS for fuel cell systems.
318
Effect of Load Modeling on Low Frequency Current Ripple in Fuel Cell Generation Systems
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Jong-Soo Kim received his B.S. degree from Seoul National University of
Technology, Seoul, Korea, in 2006,
and his M.S. degree from Sungkyunkwan University, Suwon, Korea, in 2008,
all in electrical engineering.
Since 2008, he has been working toward his Ph.D. degree in electrical engineering at Sungkyunkwan University. His research interests
include eco-friendly vehicle technologies, power conditioning systems for renewable energy and PM motor drives.
Gyu-Yeong Choe received his M.S.
degree from Sungkyunkwan University,
Suwon, Korea, in 2008, in electrical
engineering.
Since 2008, he has been working toward
his Ph.D. degree in electrical engineering
at Sungkyunkwan University. His research
interests include renewable energy
source modeling, renewable energy hybrid systems, battery
chargers for PHEV/EV and interleaved dc-dc converters.
Hyun-Soo Kang received his B.S. and
M.S. degrees from Hanyang University,
Seoul, Korea, in 1994 and 1996, respectively, and his Ph.D. degree from
Sungkyunkwan University, Suwon, Korea,
in 2008, all in electrical engineering.
From 1996 to 1999, he was an Associate
Research Engineer at Power Electronics
Lab., LGIS R&D Center, Anyang, Korea. In 2000 he
joined ADT Co., Ltd., and is now a Principal Engineer in
their R&D Center. His research interests include sensorless
drives for IM and PM motor drives, power conditioning
systems for renewable energy sources and power electronics.
Byoung-Kuk Lee received his B.S.
and the M.S. degrees from Hanyang
University, Seoul, Korea, in1994 and
1996, respectively, and his Ph.D. degree from Texas A&M University,
College Station, TX, in 2001, all in
electrical engineering.
From 2003 to 2005, he was a Senior Researcher at Power Electronics Group, KERI, Changwon,
Korea. In 2006 Dr. Lee joined the School of Information
and Communication Engineering, Sungkyunkwan University,
Suwon, Korea, as an Assistant Professor. His research interests
include electric vehicles, sensorless drives for high speed PM
motor drives, power conditioning systems for renewable energy, modeling and simulation, and power electronics.
Prof. Lee is a recipient of the Outstanding Scientists of the
21st Century from IBC and listed in the 2008 62nd Ed. of
Who’s Who in America. and 2009 26th Ed. of Who's Who
in the World. Prof. Lee is an Associate Editor of the IEEE
Transactions on Industrial Electronics and is an IEEE Senior Member.